fonts - Is it acceptable to use different but similar typefaces for print content and web content?

To be more specific, is it acceptable to have two different typefaces used for headers?

One will be used for web content and the other for print or more static content where the type won't be at the mercy of someone else's font collection.

And along these lines, is it acceptable to use two very similar typefaces for these two cases or would it be a dilution of brand identity?